What is the slope of the line?
[math]m=-\frac{2}{6}=-\frac{1}{3}[/math]
Because we do not have an integer as the y-intercept all of the time, we need to know how to get the equation for a line a different way.[br][br]So how do we write equations for these graphs?
POINT SLOPE FORMULA IS FROM THE SLOPE FORMULA!
TO USE POINT SLOPE FORMULA TO WRITE THE EQUATION FOR A LINE, ALL YOU NEED IS THE SLOPE AND ANY POINT!
What is the slope of the line in the graph?
[math]m=\frac{\left(-4\right)-0}{9-\left(-7\right)}=-\frac{4}{16}=-\frac{1}{4}[/math]
What would the equation be in point-slope form if you were using the point (-7,0)
[math]y-0=-\frac{1}{4}\left(x-\left(-7\right)\right)[/math]
Solving for y to get the equation in slope-intercept form would be...
[math]y=-\frac{1}{4}x-\frac{7}{4}[/math]
What would the equation be in point-slope form if you were using the point (9,-4)
[math]y-\left(-4\right)=-\frac{1}{4}\left(x-9\right)[/math]
Solving for y to get the equation in slope-intercept form would be...
[math]y=-\frac{1}{4}x-\frac{7}{4}[/math]
Does it matter which point you use to write your equation in point-slope form? Explain why or why not.
It does not matter which point you use because they both simplify to the same slope-intercept form, so they point slopes describe the same line.